Answer: (x - 4) (3x + 2)
Step-by-step explanation:
Factor 3x² - 10x - 8
a) Multiply the first and last coefficients: 3(-8) = -24
b) Find two numbers whose product equals -24 and sum equals -10 (the middle coefficient).
-24
∧
1 -24
2 -12 This works!
c) Replace the the middle term of -10x with 2x - 12x
3x² + 2x - 12x - 8
d) Split the equation into two sections (left and right) and factor each side separately.
3x² + 2x - 12x - 8
x(3x + 2) -4(3x + 2)
e) Notice that the parenthesis are the same. The values on the outside combine to make one of the factors and the parenthesis are the other factor.
x(3x + 2) -4(3x + 2)
= (x - 4) (3x + 2)
The logician Raymond Smullyan describes an island containing two types of people: knights who always tell the truth and knaves who always lie. You are visiting the island and have the following encounters with natives. (a) Two natives A and B address you as follows. A says: Both of us are knights. B says: A is a knave.
Answer:
A is a knave
B is a knight
Step-by-step explanation:
If A is telling the truth, then both are knights and B cannot be lying. However, since B claims that A is a knave, they can't be both knights, and there is no possible way that A is a knight.
If A is knave and thus is lying, they aren't both knights. Since B claims A is a knave, his statement can be true and thus B can be knight and A will be knave.
There different kinds of puzzle. The option that is correct about the puzzle is option A which states that A is a knave and B is a knight.
This is known to be a type of progressively hard puzzle that is titled "knights and knaves" puzzles.It is known as a logic puzzles that took place on an island with two kinds of people. It is a puzzle by American mathematician and musician called Raymond Smullyan in his book written in 1978.
Note that knave often lie and thus A may be lying when He said he was a knight Since B claims A is a knave, his statement can be said to be true and thus B can be regarded as knight.
See full question below
The logician Raymond Smullyan describes an island containing two types of people: knights who always tell the truth and knaves who always lie. You are visiting the island and have the following encounters with natives. (a) Two natives A and B address you as follows. A says: Both of us are knights. B says: A is a knave.
What are A and B?
A. A is a knave and B is a knight.
B. A is a knave and A is a knight.
C. Both A and B are knights.
D. Both A and B are knaves.
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Find the mean, median, and mode of the following data set:
2, 2, 4, 3, 4, 8,5
image 30 points) math
Answer:
[tex]\pi =\frac{C}{d}[/tex]
Step-by-step explanation:
[tex]C=\pi d[/tex]
[tex]\pi =\frac{C}{d}[/tex]
Answer:
I'm not 100%sure but i'm think that it is c
Step-by-step explanation:
Hope this helps! May have gotten it wrong really sorry if I did
Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages? Use the empirical rule.Enter your answer as a percent rounded to two decimal places if necessary.
Answer:
2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 185
Standard deviation = 26
The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.
What is the probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages?
133 = 185 - 2*26
So 133 is two standard deviations below the mean.
By the Empirical Rule, of the 50% of the measures below the mean, 95% are within 2 standard deviations of the mean, that is, above 133 and below 185. The other 5% is below 133
p = 0.05*0.5 = 0.025
2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages
Use the triangle shown on the right to complete the statement:
_____ (75*)=14.1/x
Answer: cos
2nd part: Use the equation shown to solve for the value of x. Round to the nearest tenth.
cos(75*)=14.1/x x=14.1/cos(75*)
Answer: 54.5 in
Answer:
Step-by-step explanation:
The answer is 54.5 on edg
For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
What is right angle triangle property?In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.
[tex]\rm \cos=\dfrac{ adjacent}{hypotenuse}[/tex]
Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.
The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.
Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,
[tex]\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}[/tex]
Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.
For the second part, we need to find the value of x. Thus solve the above equation further as,
[tex]\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o[/tex]
Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
Learn more about the right angle triangle property here;
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What is 80,000,000,000,000 in standard form (80 billion)
Answer:
8x10^13
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
what's the question?
it's not showing
Answer:
C.
Step-by-step explanation:
To find the perimeter, we'll use the distance formula
Distance Formula = √(x₂-x₁)²+(y₂-y₁)²
Finding Distance of AB
|AB| = √(-2+5)²+(3+1)²
|AB| = √25
|AB| = 5
Now For BC
|BC| = √(6+2)²+(-3-3)²
|BC| = √(8)²+(-6)²
|BC| = √100
|BC| = 10
FOR CA:
|CA| = √(-5-6)²+(-3+1)²
|CA| = √125
Perimeter of Triangle = 10 + 5 + √125
= 15 + √125
Please answer this correctly without making mistakes
Answer:
The perimeter is 26 yards
Step-by-step explanation:
Area of rectangle = A= l x w
1st rectangle = 6 x 5 = 30 yards squared
2nd rectangle= 10 x 3 = 30 yards squared
perimeter of rectangle = 2l+2w= 10 + 10 + 3 + 3= 26
you secure a mortgage to buy a house with a loan of $140,000 at 8.5% for 20 years. answer the following questions about that loan for the first two months of payments: a) what is the monthly payment? b)how much of the monthly payment goes toward interest when you submit your first payment? c)what is your balance after the first payment? d) how much of the monthly payment goes toward interest when you submit your second payment? e) what is your balance after the second payment?
Answer:
monthly payment $1214.951st month's interest $991.67balance after 1st payment $139,776.722nd month's interest $990.09balance after 2nd payment $139,551.86Step-by-step explanation:
The monthly interest rate is ...
[tex]\dfrac{8\%}{12}=0.00708\overline{3}[/tex]
a) The monthly payment is given by the amortization formula:
A = Pr/(1 -(1+r)^-n)
where r is the monthly interest rate on a loan of amount P for n months.
A = $140,000(0.0070833)/(1 -(1.0070833^-240)) = $1214.95
The monthly payment is $1214.95.
__
b) The amount to interest is the product of the remaining principal and the monthly interest rate.
first month's interest = $140,000·0.0070833 = $991.67
__
c) The balance after the first payment is ...
new balance = $140,000 +991.67 -1214.95 = $139,776.72
__
d) The amount to interest for the second payment is computed the same way:
second month's interest = $139,776.72·0.00708333 = $990.09
__
e) The balance after the second payment is computed the same way:
new balance = $139,776.72 +990.09 -1214.95 = $139,551.86
The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 9,000 after 3 years. What was the initial population P0? (Round your answer to one decimal place.)
Answer:
Step-by-step explanation:
Let P be the population of the community
So the population of a community increase at a rate proportional to the number of people present at a time
That is
[tex]\frac{dp}{dt} \propto p\\\\\frac{dp}{dt} =kp\\\\ [k \texttt {is constant}]\\\\\frac{dp}{dt} -kp =0[/tex]
Solve this equation we get
[tex]p(t)=p_0e^{kt}---(1)[/tex]
where p is the present population
p₀ is the initial population
If the initial population as doubled in 5 years
that is time t = 5 years
We get
[tex]2p_o=p_oe^{5k}\\\\e^{5k}=2[/tex]
Apply In on both side to get
[tex]Ine^{5k}=In2\\\\5k=In2\\\\k=\frac{In2}{5} \\\\\therefore k=\frac{In2}{5}[/tex]
Substitute [tex]k=\frac{In2}{5}[/tex] in [tex]p(t)=p_oe^{kt}[/tex] to get
[tex]\large \boxed {p(t)=p_oe^{\frac{In2}{5}t }}[/tex]
Given that population of a community is 9000 at 3 years
substitute t = 3 in [tex]{p(t)=p_oe^{\frac{In2}{5}t }}[/tex]
[tex]p(3)=p_oe^{3 (\frac{In2}{5}) }\\\\9000=p_oe^{3 (\frac{In2}{5}) }\\\\p_o=\frac{9000}{e^{3(\frac{In2}{5} )}} \\\\=5937.8[/tex]
Therefore, the initial population is 5937.8a number when added to its one third gives 96.find the number?
Answer: 72.
Step-by-step explanation:
You can solve this by representing the number in an equation that models the problem given. I will use the variable x to represent the number:
[tex]x + \frac{1}{3}x = 96[/tex]
In the equation, I listed the number and added one-third of the same number to it to equal 96.
Now, solve:
[tex]\frac{4}{3}x = 96\\ \\x = 96 / \frac{3}{4} \\\\x = 96 * \frac{3}{4} \\\\x = 72[/tex]
The number is 72.
multiply (5 4/7) times (- 2 2/5)
Answer: -13.37
Explanation: I did it in decimals because I didn’t know if your assignment required fraction or decimal. 5 4/7= 5x7=35+4=39/7 so this means 5 4/7 is equal to 39/7. -2 2/5= -2x5=-10+2=-8/5. So it comes out to 39/7x-8/5.
A database system assigns a 32-character ID to each record, where each character is either a number from 0 to 9 or a letter from A to F. Assume that each number or letter being selected is equally likely. Find the probability that at least 20 characters in the ID are numbers. Use Excel to find the probability. Round your answer to three decimal places.
Answer:
Step-by-step explanation:
total number of digits= 10 (from 0 to 9)
total number of letters = 6 (from A to F)
probability of numbers = 10/(10+6)
= 0.625
this is a case of binomial distribution with fixed number trials
n = 32 and probability p = 0.625
we have to find probability of at least 20 numbers
Use the BINOM.DIST function in Excel to find the cumulative probability.
P(at least 20 numbers) = 1 - BINOMDIST(numbers, trials, probability,true)
setting numbers = 20-1, trials = 32 and probability = 0.625
we get
[tex]P(X \geq 20)=1 - BINOMDIST(20- 1, 32, 0.625, true) \\\\=1 -0.4219 \\\\=0.5781[/tex]
Alternatively,
The probability that there are exactly r letters can be found with binomial probability.
P = nCr pʳ qⁿ⁻ʳ
Given that n = 32, p = 5/8, and q = 3/8, you can use Excel to find each probability from r=20 to r=32, then add them all up.
P = ₃₂C₂₀ (⅝)²⁰ (⅜)³²⁻²⁰ + ₃₂C₂₁ (⅝)²¹ (⅜)³²⁻²¹ + ... + ₃₂C₃₂ (⅝)³² (⅜)³²⁻³²
P = 0.578
Write 0.00000306 in scientific notation.
Answer:
3.06×10^-6
Step-by-step explanation:
0.00000306 = 3.06×0.000001 = 3.06×10^-6
__
Your calculator or spreadsheet can display numbers in scientific notation.
clara is building a triangular garden. sh wants the length of the longest side to be be three or more than twice as long as the length of the shortest side , and the third side would be twelve feet long.
what expression could she write to determine the perimeter of the triangle iof s represents the length of the shortest side?
Answer:
s+(2s+3)+12
Step-by-step explanation:
A computer scientist is investigating the usefulness of two different design languages in improving programming tasks. Twelve expert programmers, familiar with both languages, are asked to code a standard function in both languages, and the time (in minutes) is recorded. The data follow:
Programmer Design Language 1 Design Language 2
1 17 18
2 15 14
3 21 20
4 13 11
5 18 22
6 24 21
7 15 10
8 14 13
9 21 19
10 23 24
11 13 15
12 18 20
(a) Is the assumption that the difference in coding time is normally distributed reasonable?
(b) Find a 95% confidence interval on the difference in mean coding times. Is there any indication that one design language is preferable?
(a) The assumption that the difference in coding time is normally distributed
isis not
reasonable.
(b) The 95% confidence interval is (
,
) Round your answers to 3 decimal places (e.g. 98.765).
There is no / is significant indication that one design language is preferable at a 5% significance level.
Answer:
Step-by-step explanation:
The histogram shown in the attached file show that the distribution of differences is approximately normal.
So, we can assume that the distribution is normal.
.
b)
The 95% confidence level for [tex]\mu _D=\mu_1-\mu_2[/tex] is found
[tex]\bar d \pm t_{0.025,11}\frac{S_D}{\sqrt{n} }[/tex]
[tex]=0.666667 \pm 2.201\frac{(2.964436)}{\sqrt{12} } \\\\0.666667 \pm 2.201(0.85576)\\\\=0.666667+ 1.883525474=2.5502\\\\=0.666667- 1.883525474=-1.2169\\\\=(-1.2169,2.5502)[/tex]
since 0 is in the confidence interval. we do not reject the null hypothesis.
No, there is no indication of one design language is available.
A motorboat moves across the lake at a constant speed when it begins it is which function describes the motor boats distance from the shore a Y equals 4X +50 PY equals 9X +50 CY equals negative 9X +50 DY equals negative 4X +50
2. How much time do the students in my school spend on the Internet each
night?
3. What is the height of the tallest waterslide at Wild Rides Water Park?
4. What are the cabin rental prices for each of the state parks in Kentucky?
State whether each question is a statistical question. Explain your reasoning
Answer:
Only the question 2 is a statistical question.
Step-by-step explanation:
Questions
2. How much time do the students in my school spend on the Internet each night?
3. What is the height of the tallest waterslide at Wild Rides Water Park?
4. What are the cabin rental prices for each of the state parks in Kentucky?
The question 2 is a statistical question.
Is the only question that can be answered with a parameter of a population (mean number of hours spent on the internet by the students).
The other two ask for individual values: the height of the tallest waterslide at Wild Rides Water Park, and the cabin rental prices for each of the state parks in Kentucky. This need specific values that are not statistical, but deterministic.
match each object with vocabulary word that best matches it LJM KM LMK LKM
Answer:
9 + 10 = 21 higkjiitbughu
Answer:
LMK Let me know. KM Kilometer's
Step-by-step explanation:
MTH 154 - DOBM
Homework: Homework 4B
Score: 0 of 1 pt
22 of 27 (21 complete)
V Score: 777
4.B.63
* Question H
Use the appropriate compound interest formula to compute the balance in the account afte
stated period of time
$14,000 is invested for 6 years with an APR of 5% and quarterly compounding.
Answer:
$18,862.91
Step-by-step explanation:
The appropriate formula is ...
A = P(1 +r/n)^(nt)
where P is the amount invested (14,000), r is the APR (.05), n is the number of times per year interest is compounded (4), and t is the number of years (6).
Filling in the numbers and doing the arithmetic, we get ...
A = 14,000(1 +.05/4)^(4·6) = 14,000·1.0125^24 ≈ 18,862.91
The balance after 6 years will be $18,862.91.
 any help would be great
Answer:
k = P - m - n
Step-by-step explanation:
The question is asking you to rearrange the equation so that k is alone on one side.
P = k + m + n
P - k = (k + m + n) - k
P - k = m + n
(P - k) - P = m + n - P
-k = m + n - P
-1(-k) = -1 (m + n - P)
k = -m - n + P
The equation is completely simplified so this is your answer.
StartFraction 4 over 2 EndFraction = StartFraction 5 over x EndFraction Solve the proportion for x. After using cross products, the proportion becomes the equation . Isolate the variable by dividing both sides of the equation by . x = .
Answer:
StartFraction 4 over 2 EndFraction = StartFraction 5 over x EndFraction
Solve the proportion for x.
After using cross products, the proportion becomes the equation
✔ 4x = 10
.
Isolate the variable by dividing both sides of the equation by
✔ 4
.
x = ✔ 2.5
.
The value of x is 2.5 for the given proportion.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
The proportion is given in the question, as follows:
4/2 = 5/x
Using cross-product, the proportion becomes the equation as:
4x = 2 × 5
4x = 10
Divide by 4 into both sides of the above equation,
x = 10/4
x = 2.5
Thus, the value of x is 2.5 for the given proportion.
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Write 4\dfrac{7}{10}4
10
7
4, start fraction, 7, divided by, 10, end fraction as an improper fraction.
Answer:
[tex]\frac{47}{10}[/tex]
Step-by-step explanation:
Given the mixed fraction, [tex]4\dfrac{7}{10}[/tex], to convert it to proper fraction simply means removing all traces of whole number in the fraction.
To convert will will add [tex]4[/tex] to [tex]\dfrac{7}{10}[/tex] as shown;
[tex]= 4 + \frac{7}{10}\\ = \frac{4}{1} + \frac{7}{10}\\= \frac{40+7}{10}\\ = \frac{47}{10}[/tex]
The improper form of the fraction [tex]4\frac{7}{10}[/tex] is [tex]\frac{47}{10}[/tex]
Answer:
28/10 ez
Step-by-step explanation:
in khan
A researcher studying the effect of price promotions on consumers' expectations makes up two different histories of the store price of a hypothetical brand of laundry detergent for the past year. Students in a marketing course are randomly assigned to view one or the other price history on a computer. Some students see a steady price, while others see regular promotions that temporarily cut the price. Then the students are asked what price they would expect to pay for the detergent.
Is this study an experiment? Why?A. Yes. Each subject is randomly assigned to a treatment.B. No. Each subject is randomly assigned to a treatment. C. Yes. Each subject is not randomly assigned to a treatment.D. No. Each subject is not randomly assigned to a treatment.
Answer:
A. Yes. Each subject is randomly assigned to a treatment
Step-by-step explanation:
In an experimental study design, subjects are usually grouped into one or more groups in a random manner or by chance, in order to study and ascertain the effect of a treatment.
In the study cited in the question above, students were grouped by chance it randomly into a treatment group or the other. This is typical of an experimental study where subjects are usually categorised and placed randomly in control and treatment groups.
Which of the following describe an angle with a vertex at Y?
Check all that apply.
Answer:
X
Step-by-step explanation:
X and Y make up a graph
If p=(-3,-2) and q=(1,6) are the endpoints of the diameter of a circle find the equation of the circle
Answer:
The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²
or
The equation of the circle x² + 2 x + y² - 4 y = 15
Step-by-step explanation:
Given points end Points are p(-3,-2) and q( 1,6)
The distance of two points formula
P Q = [tex]\sqrt{x_{2} - x_{1})^{2} + ((y_{2} -y_{1})^{2} }[/tex]
P Q = [tex]\sqrt{1 - (-3)^{2} + ((6 -(-2))^{2} }[/tex]
P Q = [tex]\sqrt{16+64} = \sqrt{80}[/tex]
The diameter 'd' = 2 r
2 r = √80
= [tex]\sqrt{16 X 5}[/tex]
= [tex]4 \sqrt{5}[/tex]
r = 2√5
Mid-point of two end points
[tex](\frac{x_{1} + x_{2} }{2} , \frac{y_{1} +y_{2} }{2} ) = (\frac{-3+1}{2} ,\frac{-2 +6}{2} )[/tex]
= (-1 ,2)
Mid-point of two end points = center of the circle
(h,k) = (-1 , 2)
The equation of the circle
(x -h )² +(y-k)² = r²
(x -(-1) )² +(y-(2))² = (2(√5))²
x² + 2 x + 1 + y² - 4 y + 4 = 20
x² + 2 x + y² - 4 y = 20 -5
x² + 2 x + y² - 4 y = 15
Final answer:-
The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²
or
The equation of the circle x² + 2 x + y² - 4 y = 15
Answer:
-1 , 2 , 20Step-by-step explanation:
( x - -1 ) ² + ( y - 2 ) ² = 20A line contains the points (3,1) and (-6,4). What is the equation for this line in slope-intercept form?
Answer:
y = (-1/3)x + 2
Step-by-step explanation:
Equation of line in slope-intercept form is given by
y = mx +c
where m is the slope of line
c is y intercept
Slope of line having points (x1, y1) and (x2,y2) is given by (y2-y1)/(x2-x1)
_________________________________________________
let the equation of required line be y = mx +c
Since points given are (3,1) and (-6,4)
Then, its slope is
m = 4-1/-6-3 = 3/-9 = -1/3
Thus, slope of line is m = -1/3
lets use m = -1/3 in place of m in equation y = mx +c
y = (-1/3)x + c
Since points (3,1) and (-6,4) lie on y = (-1/3)x + c , it should satisfy the this equation.
hence lets plug 3 in place of x and 1 in place of y
1 = (-1/3)3 + c
=> 1 = -1 + c
=> c = 1 +1 = 2
Thus, intercept is 2.
Thus, Equation of line in slope-intercept form is y = (-1/3)x + 2.
Evaluate 16x^0 if x= -3
Answer:
16
Step-by-step explanation:
[tex]16x^0= \\\\16(-3)^0= \\\\16(1)= \\\\16[/tex]
Hope this helps!
x = -3
[tex]A = 16.(-3)^{0} \\ x^{0} = 1\\A = 16.1 \\A = 16[/tex]
Remember that [tex]x^{0} = 1[/tex] ∀ [tex]x[/tex]
Find the required annual interest rate to the nearest tenth of a percent for $1100 to grow to $1900 if interest is compounded quarterly for 10yr. The required annual interest rate is _%?
Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 1100
A = 1900
n = 4 because it was compounded 3 times in a year and n = 12/3 = 4
t = 10 years
Therefore,.
1900 = 1100(1 + r/4)^4 × 10
1900/1100 = (1+ r/4)^40
1.73 = (1+ r/4)^40
Taking log to base 10 of both sides, it becomes
Log 1.73 = 40log(1 + 0.25r)
0.238 = 40log(1 + 0.25r)
Log(1 + 0.25r) = 0.238/40 = 0.00595
Take exponent of both sides, it becomes
10^log(1 + 0.25r) = 10^0.00595
1 + 0.25r = 1.0138
0.25r = 1.0138 - 1 = 0.0138
r = 0.0138/0.25
r = 0.0552
The The required annual interest rate is
0.0552 × 100 = 5.5%
Please answer this question !! Thank u tons !! Will give brainliest !!
Answer: D
Step-by-step explanation:
The key to finding the line perpendicular to the one given is teh slope. The slope is the opposite reciprocal of the original line.
m=3
perpendicular m=-1/3
Now that we know the slope, we can see which of our answer choices have -1/3 as the slope. We can see D is the only option that has -1/3 for slope.
Answer:
D) y = -1/3x - 4
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes. This means that since the slope of this line is 3, the slope of a line perpendicular to it would be -1/3 because:
Original slope: 3 (3/1)
Reciprocal (flipped): 1/3
Negative reciprocal (opposite sign): -1/3
The only equation with a slope of -1/3 is D. Therefore, that is the correct answer.
Hope this helps!